The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.
The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.
Distributing quantum entanglements over long distances is essential for the realization of a global scale quantum Internet. Most of the prior work and proposals assume an on-demand distribution of entanglements which may result in significant network resource under-utilization. In this work, we introduce Quantum Overlay Networks (QONs) for efficient entanglement distribution in quantum networks. When the demand to create end-to-end user entanglements is low, QONs can generate and store maximally entangled Bell pairs (EPR pairs) at specific overlay storage nodes of the network. Later, during peak demands, requests can be served by performing entanglement swaps either over a direct path from the network or over a path using the storage nodes. We solve the link entanglement and storage resource allocation problem in such a QON using a centralized optimization framework. We evaluate the performance of our proposed QON architecture over a wide number of network topologies under various settings using extensive simulation experiments. Our results demonstrate that QONs fare well by a factor of 40% with respect to meeting surge and changing demands compared to traditional non-overlay proposals. QONs also show significant improvement in terms of average entanglement request service delay over non-overlay approaches.
In Quantum Local Area Networks (QLANs) - the near-term building block of the Quantum Internet - the choice of the physical network topology is not so restrictive and binding as in classical LAN in terms of communication capabilities among the network nodes. And the rationale for this is the entanglement-enabled connectivity induced by multipartite entangled states. Indeed, it is possible to create on-demand links between the QLAN nodes by properly manipulating the shared multipartite entangled states. Thus, it is possible to build an overlay entangled network upon the physical one, characterized by a topology different from the physical one and referred to as artificial topology. In this paper we address the fundamental issue of engineering the artificial topology to bypass the limitations induced by the physical network topology. This possibility to overcome the constraints in the network design induced by the physical topology has no counterpart in classical networks. To this aim, we exploit the properties of a class of multipartite entangled states, referred to as graph states, which exhibit unique properties, making them very interesting and promising for engineering artificial topologies in QLANs.
A quantum network promises to enable long distance quantum communication, and assemble small quantum devices into a large quantum computing cluster. Each network node can thereby be seen as a small few qubit quantum computer. Qubits can be sent over direct physical links connecting nearby quantum nodes, or by means of teleportation over pre-established entanglement amongst distant network nodes. Such pre-shared entanglement effectively forms a shortcut - a virtual quantum link - which can be used exactly once. Here, we present an abstraction of a quantum network that allows ideas from computer science to be applied to the problem of routing qubits, and manage entanglement in the network. Specifically, we consider a scenario in which each quantum network node can create EPR pairs with its immediate neighbours over a physical connection, and perform entanglement swapping operations in order to create long distance virtual quantum links. We proceed to discuss the features unique to quantum networks, which call for the development of new routing techniques. As an example, we present two simple hierarchical routing schemes for a quantum network of N nodes for a ring and sphere topology. For these topologies we present efficient routing algorithms requiring O(log N) qubits to be stored at each network node, O(polylog N) time and space to perform routing decisions, and O(log N) timesteps to replenish the virtual quantum links in a model of entanglement generation.
Scaling the number of entangled nodes in a quantum network is a challenge with significant implications for quantum computing, clock synchronisation, secure communications, and quantum sensing. In a quantum network, photons interact with matter qubits at different nodes, flexibly enabling the creation of remote entanglement between them. Multipartite entanglement among multiple nodes will be crucial for many proposed quantum network applications, including quantum computational tasks and quantum metrology. To date, experimental efforts have primarily focused on generating bipartite entanglement between nodes, which is widely regarded as the fundamental quantum resource for quantum networks. However, relying exclusively on bipartite entanglement to form more complex multipartite entanglement introduces several challenges. These include the need for ancillary qubits, extensive local entangling operations which increases the preparation latency, and increasingly stringent requirements on coherence times as the number of nodes grows. Here, we analyse various schemes that achieve multipartite entanglement between nodes in a single step, bypassing the need for multiple rounds of bipartite entanglement. We demonstrate that different schemes can produce distinct multipartite entangled states, with varying fidelity and generation rates. Additionally, we discuss the applicability of these schemes across different experimental platforms, highlighting their primary advantages and disadvantages.
The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through aggregate performance over all node pairs, as well as locally, at the level of individual nodes. Since entanglement-based connections form a layer above the underlying physical topology, quantum connectivity is not adequately captured by classical topological connectivity metrics. To enable characterisation of the quantum connectivity at the level of the network (or its subnetworks), we introduce the quantum connectivity measure (QCM), which quantifies the average connection quality between pairs of network nodes. Further, we describe two quantities, the quantum-connected fraction (QCF) and the quantum clustering coefficient (QCC), naturally derived from the QCM, which capture important features of the functional connectivity of the quantum network at the level of the network and an individual node, respectively. These metrics of quantum connectivity depend crucially on the entanglement distribution protocol and the quantum network parameters in addition to its physical topology. We demonstrate the crucial distinction between topological and quantum connectivity, showing that even a fully connected graph can be functionally disconnected for quantum tasks if average network edge-concurrence falls below a critical threshold. These quantum connectivity metrics thus provide important tools for the design, optimization, and benchmarking of future quantum networks.
Entanglement is unanimously recognized as the key communication resource of the Quantum Internet. Thus, the possibility of implementing unparalleled network functionalities by exploiting entanglement is gaining huge attention. However, the research efforts in this context are mainly focused onbipartite entanglement, often discarding the wide unexplored classes of entanglement shared among more than two parties, known asmultipartite entanglement. In this paper, we aim at exploiting multipartite entanglement asinter-network resource. Specifically, we consider the interconnection of different Quantum Local Area Networks (QLANs), and we show that multipartite entanglement allows to dynamically generate an inter-QLANartificialtopology, by means of local operations only, that overcomes the limitations of the physical QLAN topologies. To this aim, we first design the multipartite entangled state to be distributed within each QLAN. Then, we show how such a state can be engineered to: i) interconnect nodes belonging to different QLANs, and ii) dynamically adapt to different inter-QLAN traffic demands. Our contribution aims at providing the network engineering community with a hands-on guideline towards the concept of artificial topology and artificial neighborhood.